We study the behaviour of the Lorentzian Engle-Pereira-Rovelli-Livine
spinfoam amplitude with homogeneous boundary data, under a graph refinement
going from five to twenty boundary tetrahedra. This can be interpreted as a
wave function of the universe, for which we compute boundary geometrical
operators, correlation functions and entanglement entropy. The numerical
calculation is made possible by adapting the Metropolis-Hastings algorithm,
along with recently developed computational methods appropriate for the deep
quantum regime. We confirm that the transition amplitudes are stable against
such refinement. We find that the average boundary geometry does not change,
but the new degrees of freedom correct the quantum fluctuations of the boundary
and the correlations between spatial patches. The expectation values are
compatible with their geometrical interpretation and the correlations between
neighbouring patches decay when computed across different spinfoam vertices.
